New subclass of <em>q</em>-starlike functions associated with generalized conic domain

Xiaoli Zhang; Shahid Khan; Saqib Hussain; Huo Tang; Zahid Shareef; Xiaoli Zhang; Shahid Khan; Saqib Hussain; Huo Tang; Zahid Shareef

doi:10.3934/math.2020308

AIMS Mathematics

2020, Volume 5, Issue 5: 4830-4848. doi: 10.3934/math.2020308

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Research article

New subclass of q-starlike functions associated with generalized conic domain

1.
School of Mathematics and Computer Sciences, Chifeng University, Chifeng 024000, Inner Mongolia, People’s Republic of China
2.
Department of Mathematics, Riphah International University, 44000 Islamabad, Pakistan
3.
Department of Mathematics, COMSATS University Islamabad, Abbottabad campus 22060, Pakistan
4.
Mathematics and Natural Science division, Higher Colleges of Technology, Fujairah Men’s, Fujairah, United Arab Emirates

Received: 27 February 2020 Accepted: 20 May 2020 Published: 02 June 2020
MSC : 30C45, 30C50

In this paper, the concepts of quantum (or q-) calculus and conic regions are combined to define a new domain Ω_{k, q, γ} which represents the generalized conic regions. Then by using a certain generalized conic domain Ω_{k, q, γ} we define and investigate a new subclass of normalized analytic functions in open unit disk E. We also investigate a number of useful properties and characteristics of this subclass such as, structural formula, necessary and sufficient condition, coefficient estimates, Feketo-Szego problem, distortion inequalities, closure theorem, and subordination result. We also highlight some known consequences of our main results as corollaries.
- analytic functions,
- quantum (or q-) calculus,
- q-derivative operator,
- q-starlike functions,
- conic and generalized conic domains,
- subordination
Citation: Xiaoli Zhang, Shahid Khan, Saqib Hussain, Huo Tang, Zahid Shareef. New subclass of q-starlike functions associated with generalized conic domain[J]. AIMS Mathematics, 2020, 5(5): 4830-4848. doi: 10.3934/math.2020308

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Abstract

In this paper, the concepts of quantum (or q-) calculus and conic regions are combined to define a new domain Ω_{k, q, γ} which represents the generalized conic regions. Then by using a certain generalized conic domain Ω_{k, q, γ} we define and investigate a new subclass of normalized analytic functions in open unit disk E. We also investigate a number of useful properties and characteristics of this subclass such as, structural formula, necessary and sufficient condition, coefficient estimates, Feketo-Szego problem, distortion inequalities, closure theorem, and subordination result. We also highlight some known consequences of our main results as corollaries.

References

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